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| Variational Bayesian data analysis on manifold |
| YangMING |
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| (Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
University of Chinese Academy of Sciences, Beijing 100190, China) |
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| 摘要: |
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| 关键词: |
| DOI：https://doi.org/10.1007/s11768-018-8083-4 |
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| 基金项目:This work was supported by the National Key Research and Development Program of China (No. 2016YF-B0901900) and the National Natural Science Foundation of China (Nos. 61733018, 61333001, 61573344). |
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| Variational Bayesian data analysis on manifold |
| Yang MING |
| (Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
University of Chinese Academy of Sciences, Beijing 100190, China) |
| Abstract: |
| In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first
proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then
the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes: variational
Bayesian expectation (VB-E) step and variational Bayesian maximum (VB-M) step. Moreover, the effective of different metrics for
Bayesian analysis is discussed. |
| Key words: Variational Bayesian, Lie group, data analysis |
